### 稳定自适应神经网络控制

《stable adaptive nn control》稳定自适应神经网络控制，这本书在springer上卖300多美元，不过真的相当有用！
I do not hno hat /may appear to the world, but to myself seem to have been only like a boy playing on the seashore, diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean o lyulh lay all undiscovered before tIe V111 Contents 1 Introduction 1.1 Introduction 1.2 Adaptive Control 2 1. 3 Neural Nctwork Control 1.4 Instability Mechanisms in Adaptive Neural Control Systems 1.5 Outline of the book 8 1. 6 Conclusion 10 2 Mathematical preliminaries 11 2.1 Introduction 2.2 Mathematical preliminaries 2.2.1 Norms for Vectors and signals 12 2.2.2 Properlies of Mair 15 2.3 Concepts of Stability 16 2.4 Stability the 17 2.5 Usefull theorems and formula 19 2.5.1Sli 9 2.5.2 Mean Value Theorem 20 2.5.3 Integral Formula 20 2.5.4 Implicit Function Theorem 24 2.5.5 Dierential I 26 2.6 Conclusion 26 3 Neural Networks and Function Approximation 27 3.1 Introduct 27 3.2 Function Approximation 27 3.3 Linearly parametrized Neural Networ ks 29 3.4 Nol-linearly p rized networks 35 3.5 Neural Networks for Control applications 44 3.6 Conclusion 46 4 SISO Nonlinear Systems 47 4.1 Introduction 47 4. 2 NN Control with Regional Stability 49 4.2. 1 Desired Feedback Control 49 4.2.2 HONN Controlor Design Bascd on(4.7 51 4.2.3 MNN Control Based on(4.10) 59 4.3 VSC- Semi-Global stability 70 4.3.1 VSC-based Adaptive Nn Control design 73 4.3.2 Elimination for Controller Chattering 76 4.3.3 Simulation Study 78 4.4 Conclusio 79 5 ILF for Adaptive Control 81 5. 1 Introduction 5.2 Matching SISO Nonlinear Systems 8 5.2.1 Integral l 83 5.2.2 Choice of Weighting Function a(a) 5.2.3 Adaptive nn Control Based on DFCs 92 5.3 Backstepping Adaptive NN Design 105 5.3.1 Adaptive Design for a First-order System 108 5.3.2 Design for rtll-order SysLellIs 112 5.3.3 Controller Design with Reduced Knowledge 121 5.3.4 Simulation studie 5.4 NN Control for MIMO Nonlinear Systems 123 127 5.4.1 System Description 128 5.4.2 Lyapunov Function Design and Control Structure 129 5.4.3 Adaptive MIMo Control Using MNNs.......... 132 5.5 Conclusion 137 6 Non-affine Nonlinear Systems 139 6.1 Introductie 6.2 System Description and Properties 139 140 6.2.1 Implicit Desired Feedback Control 142 6.2.2 High-gain Observer 146 6.3 Controller Design Based on LPNn 147 6.3.1 State Feedback Control 149 6.3.2 Output Feedback Control 153 6.3.3 Simulation Study 59 6.4 Controller Design based on mnn 160 6. 4. 1 State Feedback control 162 6.4.2 Output Feedback Control 167 6.4.3 Application to CStr 176 Preface 6.5 Conclusion 8 7 Triangular Nonlinear Systems 183 7.1 Introduction 7. 2 Spccial Systems in Strict-Fccdback Form 185 7. 2. 1 Direct Adaptive NN Conti 7. 2.2 Simulation studies 198 7. 3 Partially K 200 7.3.1 Adaptive Neural Control Design 7. 3.2 Nulnerical simulation 215 7.4 Pure-feedback Nonlinear Systems 217 7.4.1 Direct Adaptive NN Control for >1 7.4.2 Direct Adaptive NN Control for 22 235 7.4.3 Simulation studies 240 7.5 MIMO Nonlinear Systems 42 7.5.1 Direct Adaptive NN Control of >1 244 7.5.2 Control of partially Known MIMo Syslels 259 7. 6 Conclusion 268 8 Conclusion 269 8.1 Conclusion 269 8.2上 urther research 270 Bibliography 271 ndex 287 X11 Preface P reface Recent years have seen a rapid development of neural network control tech niques and their successful applications. Numerous simulation studies and actual industrial implementations show that artificial neural network is a good candidate for function approximation and control system design in solving the control problems of complex nonlinear systems in the presence of different kinds of unccrtaintics. Many control approachcs /mcthods, reporting inventions control applications within the fields of adaptive control, neural contro fuzzy systems, have been published in various books, journals and conference proceedings. In spite of these remarkable advances in neural control field. due lo the complexity of nonlinear systens, the present research on adaptive neural control is still focused on the developinent of fundamental meThodologies. From a theoretical viewpoint, there is, in general, lack of a firmly mathematical basis in stability, robustness, and pcrformance analysis of neural nctwork adaptive control systems This book is motivated by the need for sysleinalic design approaches [or stable adaptive control using approximation-based techniques. The main ob jectives of the book are to develop stable adaptive neural control strategies and to pcrform transient performancc analysis of the resulted neural control systems analyticall Stability is one of the lost imporLant issues being concerned if an adaptive neural network controller is to be used in practical applications. In this book Lyapunov stability tcchniques play a critical rolc in the dcsign and stability analysis of the adaptive systcms. Under diffcrcnt opcrating conditions and a priori knowledge, stable neural controller designs are presented for several classes of nonlinear systems, including ( i) single-input single-output(SISO) nonlinear systems, (ii) nonlinear systems in strict-feedback form, (iii) nonaffine nonlinear systens, and (iv)multi-input and mulli-oulput (MIMO) nonlinear in triangular form. Stability of the overall neural network systems is rigorously proven through Lyapunov stability analysis. Transient performance of adaptive neural control systems is also essential for the control applications. It has been shown that poor initial conditions may result in unacceptably poor transient X111 Preface behaviour in adaptive systems. It is highly desirable for a control engineer to have an estimate of the transient performance before a neural network con troller is put into practice. In this book, for different neural control designs, the effects of controller parameters, initial conditions and reference signals on sys tem stability and control performance are investigated for providing valuable insights into performance improvement and design trade-offs The main special features of this book are as follows: (i) singularity-free controllers are presented for a class of nonlinear SISO systems by exploiting its property of ab(c )/aIn=0,(ii)through the introduction of integral Lya punov Lunction (ILF) candidates. novel design Inlethodologies are inlroduced to solve the control problems for a wide class of nonlinear adaptive control problems without encountering the controller singularity problem, (ii) besides affine nonlincar systcms, controllor dcsign for nonaffine nonlincar systcms arc also be treated using implicit function theorem, neural network approxima- tion and adaptive control techniques, and (iv) most of the results presented are analytical with repeatable design algorithms because closed-loop stabilit is proven mathematically, and detailed performance analysis of the proposed adaptive neural controllers is performed rigorous The book starts with a brief introduction of adaptive control, neural network control, and the possible instability mechanisms in adaptive neural control systems in Chapter 1 For completeness, Chapter 2 gives a brief sullllnary of the basic Illathe matical tools of norms, stability theorems, implicit function and mean value theorems and propcrtics of integrations, which arc used for controller design stability and performance analysis in the subsequent chapters of the book Chapter 3 presents two classes of function approximators, namely, linearly parameterized neural networks(LPNN) and non-linearly parameterized (mulli- layer)neural networks(MNN) for function approximation. Main properties of such two kinds of networks are discussed for control applications. In addition thcir advantages and shortcomings arc studicd when thcy arc uscd in system identification and adaptive control design In Chapter 4, a regionally stable nn design is firstly proposed for nonlin ear systems in a Brunovsky form. The control performance of the systems is analytically quantified by the mean square criterion and Lox criterion. Then, a semi-global nn controller is provided by using variable structure control tech nique. Furthermore, the transient bchaviour of thc adaptive neural system has been investigated, and several met hods are provided for improving the system response In Chapter 5, by introducing an integral Lyapunov function, adaptive NN controller is firstly developed for a class of SISO nonlinear systems. The con- trol singularity problem, which usually met in feedback linearization adaptive control, is completely solved using the newly proposed control method. The Preface developed control schemes ensure global stability of the adaptive systems and asymptotic convergence of output tracking error. Then, adaptive control design is developed for strict-feedback nonlinear systems through combining multilayer NNs with backstepping technique. It is proven that under certain conditions the semi-globally uniformly ultimate boundedness is achievable for the closed- loop adaptive systems. The relationship between the transient performance and the design paramctcrs is also investigatcd to guidc the tuning of the neural controller. Finally, adaptive NN Control is presented for a class of MIMO non linear systems having triangular structure in control inputs using multi-layer neural networks. Without imposing any constraints on the system interconnec tions. the developed controller guarantees the stability of the adaptive neural sysle and the convergence of the nean square tracking errors lo SImall residual In Chapter 6, adaptive Nn control is investigated for a class of nonaffine nonlinear systems. Both state and output(using a high-gain observer for state estimation)feedback controllers are given for linearly parameterized and nul- tilayer neural networks, and their effectiveness are verified by numerical simu- lation In Chapter 7, cOntroller design is investigated for several classes of triall gular nonlinear systems using quadratic Lyapunov function for its convenience of analysis and simplicity of the resulting controllers. Firstly, we investigate a class of systems in strict-feedback form with 9n(an-1) which is indepen dent of m. This nice properties can be exploited for better controller design Secondly, we study the nonlinear strict-feedhack systems which include both parametric uncertainty and unknown nonlinear functions, and constant gi so that the parametric certainties can be solved us del based adaptive col Lrol techniques and the unknown nonlinear lunctions be approximated using nN approximation. Thirdly, we investigate the control problem a class of non linear pure-feedback systems with unknown nonlinear functions. This problem is considcrcd difficult to be dealt with in the control litcraturc, mainly bccausc that the triangular structure of pure-feedback systems has no affine appear ance of the variables to be used as virtual controls. Finally, the extension from Siso nonlinear systems in triangular forms to MIMO nonlinear systems in block-triangular forms have also been considered in this chapter In summary, this book covers the analysis and design of neural network based adaptive controller for different classes of nonlinear systems, which in clude Siso nonlinear systems, nonlinear systems in strict-feedback and pure feedback forins, MIMO nOnlinear systems in triangular forIn, and nonaffine nonlinear systems. Numerical simulation studies are used to verify the effec tiveness and the performance of the control schemes. This book is aimed at a wide readership and is a convenient and useful reference for research stu dents, academics and practicing engineers in the areas of adaptive control,

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